Note that for Newton-type optimization, Assumption REF  is standard and could be replaced by the stronger, but more frequently encountered assumptions of linear independence constraint qualification and strong second-order sufficient condition, see [1]}. Regarding Assumption REF , the goal for the following section is to show that it is satisfied for sufficiently small process noise and GP posterior covariance matrices, ensuring local convergence of Alg. REF  by Lemma REF .
